# 4. Pet Palace: Reporting results of division as fractions (A)

teaches Common Core State Standards CCSS.Math.Content.5.NF.B.3 http://corestandards.org/Math/Content/5/NF/B/3
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8

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Lesson objective: Solve problems involving fair share situations to practice reporting fractional remainders.

This lesson provides an opportunity for students to apply their knowledge and understanding of interpreting fractional remainders in a fair share situation to a real-life situation. Students are asked to create a list for the new owners of Pet Palace telling them how to evenly share the supplies left for the cats and kittens.

Key Concept students will use:

• We can interpret $$({a \over b}) \times q$$ as "a" parts of a partition of q into b equal parts.

Skills students will use:

• interpret quotients of whole numbers as a number of shares and a number of groups. (Grade 3, Unit 7, 3.OA.1.2)
• use drawings and equations to represent and solve division situational problems involving equal groups. (Grade 3, Unit 7, 3.OA.1.2)

Students engage in Mathematical Practice  8 (Look for and express regularity in repeated reasoning) as they use solve a variety of similar situations that require them to express a remainder as a fairly shared amount.

Key vocabulary:

• denominator:  the number of equal-size parts into which the whole has been partitioned. For example, in the fraction $$3 \over 8$$, 8 is the denominator.  The denominator is written below the horizontal bar in a fraction.  It is also the divisor.
• dividend: the name for the number into which you are dividing in a division problem. For example, 36 is the dividend in the equation 36 ÷ 4 = 9.
• division:   A mathematical operation based on sharing or separating into equal parts.
• divisor: the name for the number that divides another number. For example, in the equation 36 ÷ 4 = 9, the divisor is 4.
• equal: exactly the same in value
• fractional remainder: the amount left over when values are divided into equal shares, expressed as a fraction.  In the division equation 16 ÷ 3 = 5 R1 the remainder is 1, which can also be expressed as $$1 \over 3$$
• numerator: the number of equal parts being considered. For example, in the fraction $$3 \over 8$$, 3 is the numerator.  The numerator is written above the horizontal bar in a fraction.  It is also the dividend.
• quotient:  The result of dividing one number by another number. For example, in the equation 36 ÷ 4 = 9, the quotient is 9.
• remainder: The amount left over when values are divided into equal shares. In the division equation 16 ÷ 3 = 5 R1 the remainder is 1.
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